If you needed a reminder that comprehensive immigration reform faces an uphill climb in the House of Representatives, look no further than the words of two members who have been working on the issue for years.

Rep. Mario Diaz-Balart (R-Fla.), who's helping craft an immigration bill in the House, said Friday that the Senate's passage of a sweeping immigration reform bill won't spur the lower chamber to act.

"The assumption that because there is a Senate bill, individual members of the House will feel pressure to support that bill frankly just is not inaccurate," Diaz-Balart said at an event in Washington sponsored by the National Restaurant Association and Bloomberg Government.

The Florida lawmaker believes the House can pass a bipartisan, comprehensive immigration reform bill. But it will have to be a bill that's generated in the GOP-controlled body. That's a tough task considering that many House Republicans remain opposed to a path to citizenship for undocumented immigrants, a must for President Obama and Democrats.

"I think the real pressure is the pressure to fix an immigration system that's broken," he added. "That's the pressure that needs to come to bear."

President Obama spoke with House Speaker John Boehner (R-Ohio) and Democratic leader Nancy Pelosi (Calif.) on Thursday night following the Senate's passage of their bill and urged them to take up the reform.

But it won't be that easy.

Boehner has already said he won't bring up a bill without the majority support of his fellow Republicans. And Diaz-Balart echoed many of his GOP colleagues that the Senate's bill is going nowhere on the other side of the Capitol.

But one of his Democratic counterparts and he both expressed optimism that a long-awaited comprehensive bill being crafted in the House could have a positive impact on the debate.

"There is time for this product to be part of the process," said Rep. Zoe Lofgren (D-Calif.), who is helping negotiate a comprehensive bill with Diaz-Balart and a group of five other bipartisan lawmakers.

Both members of Congress declined to discuss specific details of the bill, which have been kept quiet for months. But they did allude to some broad components of their proposal. It would contain some path to legalization for the 11 million undocumented immigrants living in the U.S. (they wouldn't say if it's a full path to citizenship), beefed-up border security, a new high-skilled worker visa program, and measures to verify the immigration status of job applicants.

Lofgren and Diaz-Balart also would not reveal when they plan to release their bill or whether the House could pass its own bill before lawmakers head home for August recess.

"We have not been fixated on deadlines," said the Florida Republican.

But you could sense that the uncertainty in the House has resulted in some frustration.

Lofgren, who sits on the House Judiciary Committee that oversees immigration law, ripped an effort by some House Republicans to deal with the issue on a piece-by-piece basis. She said the strategy has resulted in "small-bore partisan bills that are in some cases are bizarre."

The bills have mostly focused on stringent enforcement measures and "we have not touched the whole issue of how you get 11 million people right with the law," she said.

At the end of the day, she said, it will be up to GOP leaders like Boehner to decide whether the House will produce a bill that can reach the president's desk and become law.

"The path forward is a decision that the Republican leadership needs to make," she said. "I can't make it for them."